Solve the system of equations.

Question

3x+y=2
7x−4y=30 (1 point)
Responses

(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis

(2, −2)

Answer 1

To solve the system of equations, we can use the method of substitution or elimination.

Using the substitution method, we can solve one equation for one variable and then substitute that expression into the other equation.

From the first equation, we can solve for y in terms of x:

3x + y = 2
y = 2 - 3x

Now we substitute this value of y into the second equation:

7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2

Now we substitute this value of x back into the first equation to solve for y:

3(2) + y = 2
6 + y = 2
y = -4

Therefore, the solution to the system of equations is (2, -4).